Add the melon, cucumber, 1/4 cup lime juice and mint to a blender or food processor with 1/2 cup water. Blend until a smooth consistency.
Add another 1/2 cup of water if necessary and taste if more lime juice or honey is needed.
At this point you can either serve over ice and enjoy or strain into a pitcher for a thinner consistency.
Keep any leftovers in the refrigerator for up to about 3-4 days.
*This would also be good with cantaloup or watermelon.
*You can make this a light and refreshing cocktail with a little rum or vodka.